Analysis of Variance
Department of Educational Psychology
Agenda
1 Overview and Introduction
2 Null and Alternative Hypotheses
3 Outcomes and the Type I and Type II Errors
4 Probability Distribution Needed for Hypothesis Testing
5 Rare Events, the Sample, Decision, and Conclusion
6 Conclusion
In statistics, hypothesis testing is the process by which we evaluate whether data supports making a certain conclusion beyond a reasonable doubt
We have certain steps to work through a hypothesis test:
Agenda
1 Overview and Introduction
2 Null and Alternative Hypotheses
3 Outcomes and the Type I and Type II Errors
4 Probability Distribution Needed for Hypothesis Testing
5 Rare Events, the Sample, Decision, and Conclusion
6 Conclusion
Agenda
1 Overview and Introduction
2 Null and Alternative Hypotheses
3 Outcomes and the Type I and Type II Errors
4 Probability Distribution Needed for Hypothesis Testing
5 Rare Events, the Sample, Decision, and Conclusion
6 Conclusion
| Reality (Truth) | Decision: Reject H₀ | Decision: Fail to Reject H₀ |
|---|---|---|
| H₀ is True | Type I Error (α) False positive | Correct Decision (True negative) |
| H₁ is True | Correct Decision (True positive) | Type II Error (β) False negative |
Agenda
1 Overview and Introduction
2 Null and Alternative Hypotheses
3 Outcomes and the Type I and Type II Errors
4 Probability Distribution Needed for Hypothesis Testing
5 Rare Events, the Sample, Decision, and Conclusion
6 Conclusion
An assumption is some prerequisite of the distribution we are using
Take for example: the z-test for a population mean with the normal distribution. We need:
Agenda
1 Overview and Introduction
2 Null and Alternative Hypotheses
3 Outcomes and the Type I and Type II Errors
4 Probability Distribution Needed for Hypothesis Testing
5 Rare Events, the Sample, Decision, and Conclusion
6 Conclusion
Agenda
1 Overview and Introduction
2 Null and Alternative Hypotheses
3 Outcomes and the Type I and Type II Errors
4 Probability Distribution Needed for Hypothesis Testing
5 Rare Events, the Sample, Decision, and Conclusion
6 Conclusion
Hypothesis testing is the backbone of inferential statistics, and testing against the null hypothesis is how we determine whether our results were just a chance “fluke” or likely some real difference!
Proper hypothesis testing hinges upon wise identification of what values we have and what distribution best describes our variables. Each distribution and test we could use has a set of assumptions we need to be aware of
P-values, alpha, beta, and the two hypotheses are all connected, and we must be careful to make the correct decisions - wary of the relative risk of Type I and Type II errors
Module 9 Lecture - Repeated Measures ANOVA || Analysis of Variance